{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6, demo 3\n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "Posterior predictive checking  \n",
    "Light speed example with a poorly chosen test statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import preliz as pz\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# data\n",
    "data_path = os.path.abspath(\n",
    "    os.path.join(\n",
    "        os.path.pardir,\n",
    "        'utilities_and_data',\n",
    "        'light.txt'\n",
    "    )\n",
    ")\n",
    "y = np.loadtxt(data_path)\n",
    "# sufficient statistics\n",
    "n = len(y)\n",
    "s2 = np.var(y, ddof=1)  # Here ddof=1 is used to get the sample estimate.\n",
    "my = np.mean(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# A second example of replications\n",
    "nsamp = 1000\n",
    "pps = pz.StudentT(n-1, my, np.sqrt(s2*(1+1/n))).rvs((n, nsamp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the sample variance as a test statistic. This is a poor choice since it corresponds directly to the variance parameter in the model which has been fitted to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = np.var(pps, axis=0, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plt.hist(\n",
    "    pp,\n",
    "    20,\n",
    "    label='Variances of the replicated data sets',\n",
    "    color='C0',\n",
    ")\n",
    "plt.axvline(s2, color='C2', lw=3, label='Variance of the original data')\n",
    "plt.yticks([])\n",
    "plt.title(\n",
    "    'Light speed example with poorly chosen test statistic\\n'\n",
    "    r'$\\operatorname{Pr}(T(y_\\mathrm{rep},\\theta)\\leq T(y,\\theta)|y)=0.42$',\n",
    ")\n",
    "plt.legend(loc='center left', bbox_to_anchor=(0.7, 0.8));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
